Giuseppe Tartini - Lettere e documenti / Pisma in dokumenti / Letters and Documents - Volume / Knjiga / Volume II

257 LETTERS string), the effect will be the same. Moreover; on a table, on a stone, on a piece of metal stretch a string over a bridge: if you touch it laterally as one does on the tromba marina , the effect will be the same. Here then is the truth. But the root of this truth belongs to philosophy, not to music. To the second objection The ancient system never knew the true division of tones. My proposition is as true as the order of the number is true. If it is true (as it is universally true, and agreed upon by the ancients and the moderns) that in order to divide the 2:1 duple one must make 4:2, and the term 3 which falls in the middle thereof is the true near radical division of the duple: if it is true that to divide the sesquialter 3:2, one must make 6:4; and the term 5 which falls in the middle thereof is the true near radical division of the sesquialter: if it is true that to divide the ditone 5:4, one must make 10:9; and the term 8 which falls in the middle thereof is the true near division of the ditone, I ask: if we wish to divide the sequioctave tone 9:8, would it not be better to make 18:16, with the 17 being the true near radical division of the sesquioctave tone? Either the antecedent is true, and my result is true; or the former is not true, and so the latter is also not true. But the antecedent is undisputed, as is universally conceded by all schools; and, more than by the schools, by the immutable order of the number; and, more than by the number, by the correct institution of physical nature (concerning the root of which, if you wish for some notion in due course, I shall give it to you), therefore the result is absolutely true. Having supposed this truth, I shall come to your objection, and I tell you that not only does Doni’s 6 division have nothing to do with the system which I propose, as it is chromatic, and mine is diatonic, and because Doni’s is of one proportion and mine of a different proportion, and because Doni takes the tetrachord a to d , and I take the tetrachord to c , as the example will show, but I shall tell you something else, that Doni made a mistake in his division, as the ancients also did. If one wishes to divide a, b, the semitone of a sesqui24 proportion, it is not divided as he has done, but of 25 and 24 one makes 50 and 48, and the dividing term is 49. Now see if this division has something to do with that one, and consider which of these two is true, relating it to the comparison of all I have set forth to ascertain the order of the correct division. 6 Giovanni Battista Doni (1594-1647), an Italian classicist, philologist and music theorist. From roughly the year 1630 he devoted himself to the rediscovery of Greek music and to the revival of the ancient sounds and genres in modern musical practice. His reading of the Greek theoretical sources led him to write the Trattato de’ generi e de' modi della musica , in which he conveyed his interpretation of the ancient Greek tonal system.